The England under-21 international looks set to leave Carrow Road after Norwich's relegation from the top flight was confirmed on Wednesday.
Redmond has featured in all but three top flight fixtures for the Canaries this season, but is set to leave Carrow Road following their relegation, which despite a 4-2 win over Watford was confirmed by Sunderland's 3-0 romping of Everton on Wednesday.
Reports suggest the England under-21 international will command a fee of around £10 million, with Stoke boss Mark Hughes thought to be a particularly keen admirer.
Meanwhile, interest from West Ham has been aroused by the decision to opt against pursuing a permanent deal for Chelsea's Victor Moses, with the Hammers reportedly ready to offer wages of around £60,000 a week.
But Redmond is understood to prefer a move to Palace as he believes he is likely to get more game time at Selhurst Park, although the potential salary offered by the Eagles is likely to be lower.